The paper reports on simulations of particulate flows in square ducts with oblate and prolate particles at a bulk Reynolds number of 100 and dilute particle concentration. Inertial migration leads to focusing of particles in specific regions of the cross section. It is observed that these positions are different for the non-spherical particles compared to those obtained with spherical ones. Prolate particles exhibit Jeffery-type orbits, while oblate particles rotate around their axis of symmetry. As a result, the rotation-induced migration of prolates is much slower than for spheres and oblates. An analysis of the surrounding flow is used to show differences in the velocity field. In a second set of simulations, the particle concentration was increased by a factor of 4 with the same domain size, so that neighboring particles influence each other. The duration until focusing is achieved is substantially increased. The focusing position moves slightly to the wall, and further effects are generated. Steady particle oscillations in position are seen for spheres, and the formation of particle trains is observed in all cases. The interaction of prolate particles is particularly complex and addressed in substantial detail.